Question

Two projectiles are thrown with the same initial velocity at angles $\alpha$ and $({90}^{\circ }-\alpha )$ with the horizontal. The maximum heights attained by them are $h_1$ and $h_2$ respectively. Then $\frac{h_1}{h_2}$ is equal to

• A. ${\sin }^2\alpha$
• B. ${\cos }^2\alpha$
• C. ${\tan }^2\alpha$
• D. $1$

Answer 1

The correct option is C ${\tan }^2\alpha$

Maximum height attained is given by $h=\frac{v^2{\sin }^2\theta }{2g}$
where $\theta$ is the angle of projection with the horizontal.
So, $h_1=\frac{v^2{\sin }^2\alpha }{2g}$
and, $h_2=\frac{v^2{\sin }^2(90-\alpha )}{2g}=\frac{v^2{\cos }^2\alpha }{2g}$
$⟹\frac{h_1}{h_2}={\tan }^2\alpha$.